Every Noetherian uniformly coherent ring has dimension at most 2
A commutative ring R is said to be coherent if each finitely generated ideal of R is finitely presented. R is called uniformly coherent if for any positive integer n and any nonzero homomorphism \(f:R^ n\to R\), ker f can be generated by \(\Phi\) (n) elements, where \(\Phi\) (n) is a nonnegative integer depending only on n. Sally proved that any two- dimensional Noetherian local ring is uniformly coherent [\textit{J. D. Sally}, ''Numbers of generators of ideals in local rings'' (1978; Zbl 0395.13010)]. This paper sharpens Sally's result as well as establishing the general converse, i.e., each Noetherian uniformly coherent ring has dimension at most two.
scientific article; zbMATH DE number 3845720